The lack of suitable autologous grafts and poor compliance of existing prostheses have prompted the study of novel materials for vascular graft design. Polyurethanes (PUs) were used in the past because they have high compliance and properties that are similar to those of native tissue. In this work, the mechanical properties of a group of PUs in two states (non-hydrated and hydrated) were studied using uniaxial tensile tests, strain sweep tests, and multi-step creep recovery tests. Additionally, a hyper-elastic model based on the Mooney–Rivlin strain density function was fitted and used to model the performances of the PUs under physiological pressure and geometry conditions. The tensile tests revealed a softening phenomenon after hydration, which could potentially reduce patient discomfort and risk of vascular trauma. The ultimate strength values after hydration were similar to those reported for other vascular conduits. The strain sweep showed a strong strain dependency of the modulus indicating non-linear viscoelasticity. In the creep-recovery tests, increasing the polyethylene glycol(PEG) content enhanced the viscous flow, while the elastic behavior was enhanced with the largest concentration of polycaprolactone diol (PCL). On the other hand, under simulated physiological conditions, the compliance of the PUs showed a cyclic behavior with the time and pressure but was not affected by the radii and thickness variation, which could increase the graft compliance and geometry mismatch. Nevertheless, the compliance could be tuned using the material composition. This paper studied the biomechanics of a group of materials under simulated physiological conditions (Temperature, hydration, and pressure) to select those that could perform better for further vascular graft design.